Top Search and Quick search

I have object which have 2 fields, first is number, second is referenced to other object:

If i search use top search object with mark Resolve Reference “Cleaning in Munich” i got results:

Why i don’t see information about name/ summary but only number?

Also if i search i miss the possibility to choose in which field I would like to search for my phrase, and not only for all words written in dry text in entire objects

Should be also some filters, sorting for fields etc.

And search in objects list
can’t search by reference fields - should work (the summary or only first field in object should be treated as plain text ) and it will be work. not public ID
can’t search by public ID also
can’t search by date - should work
can’t erase my typed text - don’t have button like in top, i have to use backspace
search don’t waiting when i’m done write text and search immediately work when i write first character it should be also button like in top image or use key “enter”